Related papers: Are classical probabilities instances of quantum a…
In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
The standard picture of the loop expansion associates a factor of h-bar with each loop, suggesting that the tree diagrams are to be associated with classical physics, while loop effects are quantum mechanical in nature. We discuss examples…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
This book examines a number of problems of quantum mechanics, most of which are not usually discussed. What is the origin of probabilities in the mechanics of the microworld? What is the nature of Planck's constant h? What is the nature of…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
We study the transition between quantum and classical behavior of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of…
Here we continue with the ideas expressed in "On the strangeness of quantum mechanics" aiming to demonstrate more concretely how this philosophical outlook might be used as a key for resolving the measurement problem. We will address in…